Can someone help me to solve this : Find the equation of the tangent to the curve x^{2} -2xy + 2y^{2} -7x + 6y + 6 = 0 which is perpendicular to 6x + 5y -4 = 0
The equation 6x+ 5y- 4= 0 is the same as y= -(6/5)x+ 4/6 and has slope -6/5. The "negative reciprocal" of that is 6/5 and is the slope of the perpendicular line. I don't know where you got "45/6"! Did you mean "4/6"? Remember that the slope of the line, the number multiplying x, determines the direction, not the "constant" term.